And I just checked iTunes and it works fine there. So I guess it must be the website.

Could very well be their website. Even retail stores have problems sometimes. The Starbuck’s location that I have used before couldn’t get their Apple Pay to work yesterday. The elfish kid at the register, after fumbling around for 3 tries, finally admitted, “Well, we just had to reboot our system and some of the credit cards aren’t working...” and then one of the others acknowledged that was a problem on their end.